DOCSLIB.ORG

Velocity and Acceleration Freely Tunable Straight-Line Propagation

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Velocity and Acceleration Freely Tunable Straight-Line Propagation www.nature.com/scientificreports OPEN Velocity and acceleration freely tunable straight‑line propagation light bullet Zhaoyang Li* & Junji Kawanaka Three-dimensional (3-D) light solitons in space–time, referred to as light bullets, have many novel properties and wide applications. Here we theoretically show how the combination of difraction-free beam and ultrashort pulse spatiotemporal‑coupling enables the creation of a straight‑line propagation light bullet with freely tunable velocity and acceleration. This light bullet could propagate with a constant superluminal or subluminal velocity, and it could also counter-propagate with a very fast superluminal velocity (e.g., − 35.6c). Apart from uniform motion, an acceleration or deceleration straight‑line propagation light bullet with a tunable instantaneous acceleration could also be produced. The high controllability of the velocity and the acceleration of a straight-line propagation light bullet would enable very specifc applications, such as velocity and/or acceleration matched micromanipulation, microscopy, particle acceleration, radiation generation, and so on. Te combination of difraction-free beam and dispersion-free pulse permits the chance to produce 3-D self- similar spatiotemporal optical wave packets (light bullets), which could propagate over long distances and, importantly, maintain invariant intensity profles in space and time1–4. In nonlinear optics, the balance between nonlinearity and dispersion/difraction could easily result in temporal/spatial solitons 5–13, however some appli- cations require to generate light bullets in linear/free space. In linear optics, Bessel beam is one of the most important difraction-free beams whose central core is propagation invariant 14,15, and up to now many novel methods have already been proposed16–21, such as circular slit with lens16, axicon17, spatial light modulator18, and so on. Airy beam is another interesting difraction-free beam, and, compared with Bessel beam, its main intensity maxima and lobes could tend to accelerate during propagation along a parabolic trajectory 22–29. For a difraction-free beam, when the monochromatic wave is replaced by a dispersion-free pulse, a light bullet might be produced. Te simplest form is the Gauss-Bessel/Airy light bullet in free space (non-dispersion environment) or the Bessel/Airy-Bessel/Airy light bullet in materials (dispersion environment) 1,22,30,31. To control the velocity and even the acceleration of a light bullet is an interesting but challenging work. Previously, during a short propa- gation distance, the group velocity given by υg = c/ng could be controlled by crafing the wavelength-dependent refractive index32, however some very special material or photonic systems are necessary33–41, such as ultra-cold atoms33, hot atomic vapors35, stimulated Brillouin scattering36, active gain resonances37, tunneling junctions38, metamaterials39, photonic crystals40, and so on. Te problem is that, in transparent materials at wavelengths far from resonance or even in free space, the controllability of ng and accordingly the group velocity υg would be very limited. Light bullet with an airy beam could self-accelerate during propagation in free space, however which travels along a bended (parabolic) propagation trajectory 22–24. Recently, several spatiotemporal coupling methods have been proposed to control the group velocity of optical wave packets in free space42–46. For example by controlling temporal and spatial dispersion (temporal chirp and chromatic aberration)42,44, a fying focus with a tunable group velocity could be achieved, however the propagation distance is limited within the focusing region. In this article, we combined the frst-order spatiotemporal coupling (pulse-front pre-deformation) with the difraction-free (Gauss-Bessel) pulsed beam and theoretically produced a straight-line propagation light bullet in free space, whose velocity and acceleration could be freely controlled, including all cases of superlumi- nal, subluminal, acceleration, deceleration and backwards-traveling group velocities. We have mainly discussed the case of a Gauss-Bessel pulsed beam in free space, and the method is also suitable to other types of pulsed beams, for example the Airy-Bessel pulsed beam in free space or materials. Tis velocity and acceleration tunable straight-line propagation light bullet has lots of specifc applications from basic sciences to industry applications. Institute of Laser Engineering, Osaka University, 2-6 Yamadaoka, Suita, Osaka 565-0871, Japan. * email: [email protected] SCIENTIFIC REPORTS | (2020) 10:11481 | https://doi.org/10.1038/s41598-020-68478-1 1 Vol.:(0123456789) www.nature.com/scientificreports/ Figure 1. Gauss-Bessel light bullet with a conical-pulse-front pre-deformation. (a) Te input pulsed beam possesses a plane phase-front and a conical pulse-front, and the axicon generates a Gauss-Bessel light bullet (in free space) in the interference region. (b) Superluminal light bullet in the case of CC-CPF (α = 0.5° and β = 6.6°). Te longitudinal gap Δz (between the light bullet and the intersection of phase-fronts illustrated by white lines) decreases during propagation. (c) Subluminal light bullet in the case of CV-CPF (α = 0.5° and β = − 6.6°). Te longitudinal gap Δz increases during propagation. (d) Variation of the longitudinal gap Δz with time t. Te travelling velocity of the intersection of phase-fronts is 1.00004c, and that of the light bullet with CC-CPF of (b) and CV-CPF of (c) is 1.001c and 0.999c, respectively. Superluminal and subluminal light bullets. An axicon can transform a plane wave into a conical wave and generate a Bessel beam in the overlap region due to interference 17. In vacuum, the propagation velocity (group velocity) of this Bessel beam is υb = c/cosα, where c is the light speed in vacuum and α is the (half) conical angle (relevant to both the refractive index and the wedge angle of the axicon)47. It can be found that this veloc- ity is faster than the light speed in vacuum c, which also increases with increasing the conical angle α. Figure 1a shows the key idea of the method proposed in this article that the input pulsed beam possesses a distortion-free (plane) phase-front but a pre-deformed (conical) pulse-front, which is quite diferent from the previous case with both distortion-free (plane) phase- and pulse-fronts. It is necessary to introduce that the phase-front is the surface perpendicular to the propagation direction while the pulse-front is the surface coinciding with the peak of a pulse, which are respectively determined by the phase- and group-velocities48. Te result of the method is that the velocity of the generated light bullet could be freely controlled. As an example we begin the simulation with an initial input pulsed beam with a 30 fs (FWHM) pulse in time, a 2 mm (1/e2) beam in space and a concave conical-pulse-front (CC-CPF) in space–time, and the generation and the propagation of the light bullet in the 2-D propagation section of the x–z plane is shown in Fig. 1b. Te axicon spatially divides the input pulsed beam into two Gauss-Gauss ones and changes their travelling directions (green arrows) with symmetrical angles of α = ± 0.5°. Te phase-fronts of two pulsed beams are illustrated by white lines, and the pulse-fronts are shown by red distributions. It can be found that in the overlap region a light bullet (in free space) is generated due to inter- ference, which in time is a Gauss pulse and in space is a Bessel beam. Because the pulse-front is pre-deformed to deviate from the phase-front with a tilt angle of β = 6.6°, the generated light bullet is not located at the inter- section of the phase-fronts anymore, and we can say the light bullet is temporally or spatially delayed along the longitudinal axis. Here, we make two defnitions: in space, the propagation (longitudinal) axis of the Bessel beam is the z–axis and its geometrical center in the overlap region (formed by two pulsed beams afer the axicon) is the SCIENTIFIC REPORTS | (2020) 10:11481 | https://doi.org/10.1038/s41598-020-68478-1 2 Vol:.(1234567890) www.nature.com/scientificreports/ Figure 2. Controllability of velocity and backwards travelling light bullet. (a) Velocity of the light bullet as a function of the pulse-front tilt angle β for diferent conical angles α (α equals 0.5°, 1° & 5° in upper and 80°, 85° & 88° in lower). Te velocity is normalized by c. (b) Backwards travelling light bullet with α = 85° and β = 6.6° (spot marked in (a) lower), and the velocity is − 35.6c. Due to a large conical angle α, the light bullet is very small and most energies are transferred to the rings around the light bullet. White lines and arrows in (b) illustrate phase-fronts and propagation directions. origin of z = 0; and in time, the moment when the intersection of two phase-fronts (the original location of the light bullet if without any pulse-front pre-deformation) arriving at z = 0 is the zero time of t = 0. Figure 1b gives the detailed distributions of the pulse-fronts, the phase-fronts and the light bullet at diferent times of t = − 120, − 60, 0, 60 and 120 ps during propagation. According to the previous result41, the intersection of two phase- fronts travels at a velocity of 1.00004c governed by υb = c/cosα. However, due to the pulse-front pre-deformation, the light bullet is behind the intersection of phase-fronts and the longitudinal gap Δz (distance between the light bullet and the intersection of phase-fronts) decreases with time during propagation. Tis phenomenon indicates the travelling velocity of the light bullet is faster than that of the intersection of phase-fronts, i.e., a superluminal light bullet is produced.
Load more

Recommended publications
  • Laser-Based Optical Trap for Remote Sampling of Interplanetary And
    Laser-Based Optical Trapping for Remote Sampling of Interplanetary and Atmospheric Particulate Matter Paul Stysley (PI-Code 554 NASA- GSFC), Demetrios Poulios, Richard Kay , Barry Coyle, Greg Clarke Or Tractor Beams Not yet: Hopefully Soon: Tractor Beam Basics What is a tractor beam? Target motion Laser Direction of beam propagation Why study tractor beams? Purpose: A tractor beam system will enhance the capability of current particle collection instruments by combining in situ measurements with remote sensing missions. This would increase the range, frequency, and quantity of samples collected for many planned lander and free flyer-based systems as well enabling the creation of new Decadal Survey missions. Key Milestones and Goals Proposal Goals: (1) To fully study and model current state-of-the-art in optical trapping technology and potential for use in remote sensing measurements. (2) To determine the scalability of the optical trapping system in regards to the range, frequency, and quantity of sample collection. (3) To determine what types of particles can be captured and if species selection is possible. (4) To formulate a plan to build and test a system that will demonstrate the remote sensing capability and potential of laser-based optical trapping for NASA missions. Milestones: • Complete fundamental optical trapping study 01/2012 • Determine scalability of trapping 04/2012 • Determine particle selection constraints 07/2012 • Devise remote sensing system 09/2012 • Publish results 10/2012 TRLin = 1 Current Technology Throughout NASA’s history mission have deployed several different innovative in situ techniques to gather particulates such as Faraday traps, ablation and collection, drills, scoops, or trapping matter in aerogel then returning the samples to Earth.
    [Show full text]
  • NON-DIFFRACTING WAVES, and “FROZEN WAVES”: an Introduction(†)
    NON-DIFFRACTING WAVES, AND \FROZEN WAVES": ( ) An Introduction y Erasmo Recami INFN|Sezione di Milano, Milan, Italy; and Facolt`a di Ingegneria, Universit`a statale di Bergamo, Bergamo, Italy. and Michel Zamboni-Rached, DMO/FEEC, UNICAMP, Campinas, SP, Brazil. Abstract { This contribution is an extended presentation of the talk delivered by one of us (ER) by having recourse to simple transparencies only... In the First Part of this contribution we present simple, general and formal, introductions to the ordinary gaus- sian waves and to the Bessel waves, by explicitly separating the case of beams from the case of pulses; and, afterwards, an analogous introduction is presented for the so-called Localized Waves (LW), pulses or beams. The LWs, incidentally, ought to be rather called Non-diffracting Waves (and the title of the talk has been consequently modified). Always we stress the very different characteristics of the gaussian with respect to the Bessel waves and to the LWs, showing the numerous important properties of the latter: Properties that may find application in all fields in which an essential role is played by a wave-equation (like electromagnetism, optics, acoustics, gravitation, elementary particle physics, and in particular Seismology and Geophysics). [The First Part of this contribution ends with an Appendix, wherein: (i) we recall how, in the seventies and eighties, the geometrical meth- ods of Special Relativity (SR) predicted |in the sense below specified— the existence of the most interesting LWs, i.e., of the X-shaped pulses; and (ii) in connection with the circumstance that the X-shaped waves are endowed with Superluminal group-velocities (as discussed in the first part of this contribution), we briefly mention the various experi- mental sectors of physics in which Superluminal motions seem to appear; in particular, a bird's-eye view is presented of the experiments till now performed with evanescent waves (and/or tunnelling photons), and with the \localized Superluminal solutions" to the wave equations.
    [Show full text]
  • Bessel and Annular Beams for Materials Processing
    LASER & PHOTONICS Laser Photonics Rev. 6, No. 5, 607–621 (2012) / DOI 10.1002/lpor.201100031 REVIEWS Abstract Non-Gaussian beam profiles such as Bessel or an- nular beams enable novel approaches to modifying materials through laser-based processing. In this review paper, proper- ties, generation methods and emerging applications for non- conventional beam shapes are discussed, including Bessel, an- nular, and vortex beams. These intensity profiles have important implications in a number of technologically relevant areas includ- ing deep-hole drilling, photopolymerization and nanopatterning, and introduce a new dimension for materials optimization and fundamental studies of laser-matter interactions. ARTICLE REVIEW Bessel and annular beams for materials processing Marti Duocastella and Craig B. Arnold* 1. Introduction laser pulse duration can have a significant effect on the ma- terial removal dynamics. This leads to a more rapid ejection 1.1. General laser processing of material with a smaller heat affected zone as the temporal pulse length is shortened [12]. The control and influence of other laser parameters is Lasers have become indispensible for materials processing less common yet these can also be important factors in ma- in scientific and industrial applications. They offer a highly terials processing. One of these is the laser beam shape, directional and localized source of energy, which facilitates defined as the irradiance distribution of the light when it materials modifications at precise locations [1]. Modern arrives at the material of interest [13]. Although some laser laser systems are also flexible, in the sense that it is relatively systems emit a multimode beam with a complex intensity easy to adapt parameters such as the beam size or the beam distribution, most commercial lasers provide either a Gaus- energy to specific requirements, and systems can be scaled sian intensity profile (Fig.
    [Show full text]
  • Generation and Application of Bessel Beams in Electron Microscopy
    Generation and Application of Bessel Beams in Electron Microscopy Vincenzo Grillo 1,2 , Jérémie Harris 3, Gian Carlo Gazzadi 1, Roberto Balboni 4, Erfan Mafakheri 5, Mark R. Dennis 6, Stefano Frabboni 1,5, Robert W. Boyd 3, Ebrahim Karimi 3 1 CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena, Italy 2 CNR-IMEM Parco Area delle Scienze 37/A, I-43124 Parma, Italy 3 Department of Physics, University of Ottawa, 25 Templeton St., Ottawa, Ontario K1N 6N5, Canada 4 CNR-IMM Bologna, Via P. Gobetti 101, 40129 Bologna, Italy 5 Dipartimento di Fisica Informatica e Matematica, Università di Modena e Reggio Emilia, via G Campi 213/a, I-41125 Modena, Italy 6 H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom Abstract We report a systematic treatment of the holographic generation of electron Bessel beams, with a view to applications in electron microscopy. We describe in detail the theory underlying hologram patterning, as well as the actual electro- optical configuration used experimentally. We show that by optimizing our nanofabrication recipe, electron Bessel beams can be generated with efficiencies reaching 37±3%. We also demonstrate by tuning various hologram parameters that electron Bessel beams can be produced with many visible rings, making them ideal for interferometric applications, or in more highly localized forms with fewer rings, more suitable for imaging. We describe the settings required to tune beam localization in this way, and explore beam and hologram configurations that allow the convergences and topological charges of electron Bessel beams to be controlled.
    [Show full text]
  • Beam Shaping Optical Lens Designs for Diffraction-Free Bessel Beams
    InternationalJournal of VIBGYOR Optic and Photonic Engineering Beam Shaping Optical Lens Designs for Diffraction-Free Bessel Beams Research Article: Open Access ISSN: 2631-5092 Abdallah K Cherri* and Mahmoud K Habib Electrical Engineering Department, College of Engineering and Petroleum, Kuwait University, Kuwait Abstract Beam shaping technique is applied to design optical lenses for transforming uniform beams to diffraction-free Bessel Beams. One-lens and two-lens refracting system will be demonstrated where the lens’ surfaces equations can be easily derived. The designed lenses take the input uniform beam distribution and confine it to be within the main lobe of the Bessel beam and avoid its zeros crossings. Various design parameters such as the power of the beam and the optical system length will be discussed. It will be demonstrated that the two-element design will produce smaller system length than the one-element design. Keywords Beam shaping methods, One-element and two-element refracting system, Lens design Introduction cessing increases, researchers increase their efforts in exploring other non-Gaussian laser beams (due The fundamental mode (TEM ) of the cavity of 00 to its short, micron-sized Rayleigh range), such as Gaussian laser beam is the most common beam the non-diffracting Bessel beams [9], which have an shape used in optical processing. In particular, for accurate laser beam focusing over a good distance materials processing [1-8] the low divergence of range. This comes at the expense of reducing the the Gaussian beam provides a small focused spot. It amount of energy available in the process where can be shown that a focal spot size as small as 1 μm Gaussian beam has an advantage over any other can be obtained using a lens with a given numerical beam shape.
    [Show full text]
  • Bessel Beams That Satisfy Maxwell’S Equations Are Given in Sec
    Bessel Beams Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (June 17, 2000) 1 Problem Deduce the form of a cylindrically symmetric plane electromagnetic wave that propagates in vacuum. A scalar, azimuthally symmetric wave of frequency ω that propagates in the positive z direction could be written as − ψ(r, t)= f(ρ)ei(kzz ωt), (1) where ρ = √x2 + y2. Then, the problem is to deduce the form of the radial function f(ρ) and any relevant condition on the wave number kz, and to relate that scalar wave function to a complete solution of Maxwell’s equations. The waveform (1) has both wave velocity and group velocity equal to ω/kz. Comment on the apparent superluminal character of the wave in case that kz < k = ω/c, where c is the speed of light. 2 Solution As the desired solution for the radial wave function proves to be a Bessel function, the cylindrical plane waves have come to be called Bessel beams, following their introduction by Durnin et al. [1, 2]. The question of superluminal behavior of Bessel beams has recently been raised by Mugnai et al. [3]. Bessel beams are a realization of super-gain antennas [4, 5, 6] in the optical domain. A simple experiment to generate Bessel beams is described in [7]. Sections 2.1 and 2.2 present two methods of solution for Bessel beams that satisfy the Helmholtz wave equation. The issue of group and signal velocity for these waves is discussed in sec. 2.3. Forms of Bessel beams that satisfy Maxwell’s equations are given in sec.
    [Show full text]
  • Manipulation of Microparticles by Bessel Light Beam Tashtimirova D.U., Savchenko E.A., Aksenov E.T., and Kuptsov V.D
    PhIO-2018 KnE Energy & Physics VII International Conference on Photonics and Information Optics Volume 2018 Conference Paper Manipulation of Microparticles By Bessel Light Beam Tashtimirova D.U., Savchenko E.A., Aksenov E.T., and Kuptsov V.D. Peter the Great St. Petersburg Polytechnic University, Polytechnic Str. 29, St. Petersburg, 195251 Abstract We consider perspectives of optical manipulation of microscopic objects in the area of biology, biophysics and medicine. The first part of the work is devoted to a brief review of the microparticles’ manipulation. The second part contains calculations of the focusing of laser radiation parameters and some results on the formation of Bessel light beams. The experimental setup based on the optical manipulation technique of micron-sized particles was developed. Corresponding Author: Tashtimirova D.U. [email protected] 1. Introduction Received: 28 January 2018 Accepted: 15 March 2018 A non-contact device based on optical trapping is used to study micro- and nanopar- Published: 25 April 2018 ticles. Optical trapping is a technology that uses a tightly focused light field for manip- Publishing services provided by ulating microscopic objects, and has a delicate influence on them [1]. Recently such Knowledge E device was used in microsurgery, pharmaceutics, biophysics to study the structure and Tashtimirova D.U. et al. This operation principles of macromolecules [2] and in colloid chemistry to study objects article is distributed under the terms of the Creative Commons such as charged colloidal particles in solutions [3]. Optical tweezers are relevant, Attribution License, which because they can be used to study the elasticity of the membrane, unwinding force permits unrestricted use and redistribution provided that the of the microtubules and associated protein that plays an important role in further original author and source are understanding the kinetics of protein and cell membranes [4].
    [Show full text]
  • Laser Micro- and Nanostructuring Using Femtosecond Bessel Beams M.K
    Laser micro- and nanostructuring using femtosecond Bessel beams M.K. Bhuyan, F. Courvoisier, H.S. Phing, O. Jedrkiewicz, S. Recchia, P. Di Trapani, J.M. Dudley To cite this version: M.K. Bhuyan, F. Courvoisier, H.S. Phing, O. Jedrkiewicz, S. Recchia, et al.. Laser micro- and nanostructuring using femtosecond Bessel beams. The European Physical Journal. Special Topics, EDP Sciences, 2011, 199 (1), pp.101-110. 10.1140/epjst/e2011-01506-0. hal-00661745 HAL Id: hal-00661745 https://hal.archives-ouvertes.fr/hal-00661745 Submitted on 22 Apr 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution| 4.0 International License Laser micro- and nanostructuring using femtosecond Bessel beams M.K. Bhuyan1,2,a, F. Courvoisier2,H.S.Phing3,4, O. Jedrkiewicz1, S. Recchia5, P. Di Trapani1, and J.M. Dudley2,b 1 CNISM and Dipartimento di Fisica e Matematica, Universit`adell’Insubria, via Valleggio 11, 22100 Como, Italy 2 D´epartement d’Optique P. M. Duffieux, Institut FEMTO-ST, UMR 6174, CNRS - Universit´edeFranche-Comt´e, 16 route de Gray, 25030 Besan¸con Cedex, France 3 INRS-EMT, University of Quebec, 1650, Boul.
    [Show full text]
  • From Amorphous Speckle Pattern to Reconfigurable Bessel Beam Via
    From amorphous speckle pattern to reconfigurable Bessel beam via wavefront shaping 1,* 1 2 1 DIEGO DI BATTISTA, DANIELE ANCORA, MARCO LEONETTI, AND GIANNIS ZACHARAKIS 1Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas, N. Plastira 100, VasilikaVouton, 70013, Heraklion, Crete, Greece 2 Center forLife Nano Science@Sapienza, Instituto Italiano di Tecnologia, Viale Regina Elena, 291 00161 Rome (RM), Italy *Corresponding author: [email protected] Bessel beams are non-diffracting light structures, which Bessel beams have the property to be "self-reconstructing" can be produced with simple tabletop optical elements meaning that the light-structure is immune to scattering such as axicon lenses or ring spatial filters and coherent encountered along the beam trajectory [16], (thus enabling laser beams. One of their main characteristic is that applications such as deep laser writing [17]), but not to Bessel beams maintain their spatial characteristics after extended scattering barriers [18]. meters of propagation. In this paper we demonstrate a In this Letter we describe a method for producing Axicon system and method for generating Bessel beams from Opaque Lenses (AOL) able to combine the properties of non- amorphous speckle patterns, exploiting adaptive diffractive Bessel beams with the advantages of adaptive focusingenabling large depth of field combined with user optimization by a spatial light modulator. These speckles defined reconfigurability. are generated by light modes transmitted through a By filtering the spatial spectrum of the light transmitted at the scattering curtain and selected by a ring shaped filter. back of a scattering sample [19] with a ring-shape spatial filter With the proposed strategy it is possible to produce at we create an amorphous speckle pattern [20,21,22].
    [Show full text]
  • A Tale of Two Beams: Gaussian Beams and Bessel Beams
    A TALE OF TWO BEAMS: GAUSSIAN BEAMS AND BESSEL BEAMS ROBERT L. NOWACK∗ Abstract. An overview is given of two types of focused beams, Gaussian beams and Bessel beams. First I describe some of the basic properties of Gaussian beams in homogeneous media which stay collimated over a certain distance range after which they diverge. Bessel beams are then described which are among a class of solutions to the wave equation that are diffraction-free and do not diverge when they propagate. For pulsed signals, another solution that propagates in an undistorted fashion is called an X-wave. I will then compare and contrast these different beam solutions to the wave equation. 1. Introduction. Gaussian beams are focused wave solutions to the wave equation that stay collimated out to some distance range after which they diverge. In the 1980’s, Durnin (1987) and Durnin et al. (1987) showed that realistic beams could propagate without change of shape to a large range in comparison to Gaussian beams and were called Bessel beams. There solutions were found earlier by Stratton (1941, pp. 356), Courant and Hilbert (1966, Vol. 2, pp. 760, Bateman (1915) among others, and an overview is given in Recami et al. (2008). However, these solutions are endowed with infinite energy, similar to plane waves, and did not attract much interest at the time. In this overview, I will first describe some of the basic properties of Gaussian beams as examples of beams that diffract and then describe Bessel beams as examples of beam modes that are diffraction free. 2.
    [Show full text]
  • Light-Sheet Engineering Using the Field Synthesis Theorem
    bioRxiv preprint doi: https://doi.org/10.1101/700633; this version posted July 13, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. Light-sheet engineering using the Field Synthesis theorem Authors Bo-Jui Chang1, and Reto Fiolka1,2. Affiliation 1 – Department of Cell Biology, UT Southwestern Medical Center, Dallas, TX, USA. 2 – Lyda Hill Department of Bioinformatics, UT Southwestern Medical Center, Dallas, TX, USA. Abstract Recent advances in light-sheet microscopy have enabled sensitive imaging with high spatiotemporal resolution. However, the creation of thin light-sheets for high axial resolution is challenging, as the thickness of the sheet, field of view and confinement of the excitation need to be carefully balanced. Some of the thinnest light-sheets created so far have found little practical use as they excite too much out-of-focus fluorescence. In contrast, the most commonly used light- sheet for subcellular imaging, the square lattice, has excellent excitation confinement at the cost of lower axial resolving power. Here we leverage the recently discovered Field Synthesis theorem to create light-sheets where thickness and illumination confinement can be continuously tuned. Explicitly, we scan a line beam across a portion of an annulus mask on the back focal plane of the illumination objective, which we call it C-light-sheets. We experimentally characterize these light-sheets and their application on biological samples. Keywords Field Synthesis, lattice light-sheet, C-light-sheet Introduction Light-sheet fluorescence microscopy (LSFM) has been transformative for volumetric imaging of single cells up to entire organisms, as it minimizes sample irradiation and allows efficient and rapid 3D imaging1-3.
    [Show full text]
  • Creation of Matter Wave Bessel Beams and Observation of Quantized Circulation in a Bose–Einstein Condensate
    Home Search Collections Journals About Contact us My IOPscience Creation of matter wave Bessel beams and observation of quantized circulation in a Bose–Einstein condensate This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 New J. Phys. 16 013046 (http://iopscience.iop.org/1367-2630/16/1/013046) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 131.238.16.30 This content was downloaded on 12/08/2014 at 14:23 Please note that terms and conditions apply. Creation of matter wave Bessel beams and observation of quantized circulation in a Bose–Einstein condensate C Ryu, K C Henderson and M G Boshier1 Physics Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA E-mail: [email protected] Received 18 September 2013, revised 18 November 2013 Accepted for publication 9 December 2013 Published 23 January 2014 New Journal of Physics 16 (2014) 013046 doi:10.1088/1367-2630/16/1/013046 Abstract Bessel beams are plane waves with amplitude profiles described by Bessel functions. They are important because they propagate ‘diffraction-free’ and because they can carry orbital angular momentum. Here we report the creation of a Bessel beam of de Broglie matter waves. The Bessel beam is produced by the free evolution of a thin toroidal atomic Bose–Einstein condensate (BEC) which has been set into rotational motion. By attempting to stir it at different rotation rates, we show that the toroidal BEC can only be made to rotate at discrete, equally spaced frequencies, demonstrating that circulation is quantized in atomic BECs.
    [Show full text]